In radar of this type the frequency of the wave transmitted towards the target varies as a function of time, for example in a linear fashion. To avoid degrading the distance resolution on reception, the wave is time compressed. The filter applying this compression uses a signal which is often called a "replica".
The replica determines the performance of the radar, which is usually characterized by its impulse response. Impulse response is the response of the instrument when the signal is transmitted towards an isolated point target, without interference. Impulse response in the time domain RI(t) has the value: EQU RI(t)=s(t)*r(t),
where S(t) is the transmitted signal as a function of time, r(t) is the replica and * is the convolution product. PA1 where S(f)=F(s(t)) is the spectrum of the transmitted signal and R(f)=F(r(t)) is the spectrum of the replica. PA1 where s*(t) is the complex conjugate-of the signal s(t).
In the frequency domain: EQU RI(f)=S(f).multidot.R(f)
In the conventional case of a matched filter, which maximizes the signal to noise ratio: EQU R(t)=s*(t)
In this case, the impulse response is a sinc function (sin t)/t having an active central peak and secondary lobes that must be attenuated or eliminated as they degrade the quality of radar measurements because they can be interpreted as false targets and reduce commensurately the energy contained in the active main lobe. The usual method of attenuating the secondary lobes of the impulse response is to multiply the replica by a weighting function.
However, weighting widens the main lobe and reduces its amplitude maximum. Widening (increase in duration) degrades resolution, and reduction in amplitude degrades signal to noise ratio. To obtain the required resolution and signal to noise ratio, degradation is compensated by increasing the transmitted frequency band and transmitter power. The radar is therefore complex and costly. Also, the far lobes, also known as Fresnel lobes, are not attenuated significantly because the level of these lobes is -20.log(BT)+3 dB away from the maximum of the main lobe, B being the bandwidth of the transmitted signal and T the duration of the transmitted pulse.
To attenuate the Fresnel lobes, the transmitted signals depart from a signal with simple linear variation of frequency. This also increases the complexity of the radar because it increases the bandwidth of the signals transmitted and received.